This invention relates to pulsed power machines and systems. More particularly, this invention relates to plasma opening switches that typically connect the pulse forming and storage stages of an inductive energy storage system to the output load in a very short time interval. Still more particularly, this invention relates to a command triggered, two stage plasma opening switch (POS).
The well-known advantages of inductive energy storage could allow smaller and more efficient pulsed-power drivers. Inductive energy storage systems allow lower voltage at the vacuum interface; the water pulse-compression elements and vacuum interface are significant cost and size items in high-power drivers. Because the opening switch is the point of highest voltage in an inductive storage design, it is the single most important part of such systems. An efficient opening switch that operates in vacuum, close to the load would have many applications. Such a switch can use the inductance associated with the vacuum interface to advantage as energy storage.
Since its invention, the plasma opening switch (see C. W. Mendel, Jr. and S. A. Goldstein, "A fast-opening switch for use in REB diode experiments," J. AppI Phys., vol. 48, pp. 1004-1006, 1977) has been studied as an attractive pulse-compression element for pulsed-power applications (see "Special issue on fast opening vacuum switches," IEEE Trans. Plasma Sci., vol. PS-15, 1987). A POS exploits the fact that plasma is an excellent conductor with low mass. The mass is important because the plasma must be moved rapidly to open the switch, and lower mass conductors require less energy to move quickly. The fact that the POS operates in vacuum also allows magnetic insulation, with higher insulation strength than any other dielectric.
Though widely studied, application of the plasma opening switch has met with limited success in demanding applications (those requiring both long conduction and fast opening). One basic reason is the lack of a strong, abrupt mechanism for opening in the standard POS. The only force at work in the standard POS is the drive current magnetic field. This field is slow-rising compared to the desired opening time, and is almost constant near peak current (maximum stored energy). For opening, rapid removal of plasma from the switch region is necessary. An independent mechanism that quickly removes plasma from the switch region would improve POS performance.
The advantages of a command-triggered switch are clear. In particular, since a POS will be the final stage of pulse compression, command-triggering would assure low jitter from the POS, and removal of jitter from upstream elements. This is unique; command triggering of the final pulse compression stage has not been demonstrated in large pulsers using water-dielectric closing switches or elsewhere.
The standard POS is realized by injecting plasma from an external plasma source into the anode-cathode gap of a magnetically insulated transmission line. FIG. 1 shows schematically a simplified plasma opening switch.
The plasma short-circuits the transmission line, allowing magnetic energy to accumulate in the storage inductance upstream of the plasma opening switch. When the POS opens, the stored magnetic energy transfers to the load. There are two effects that cause the initially closed POS to open. First, there is a magnetic pressure from the storage inductor current pushing on the plasma (which has no tensile or shear strength). Second, there is ion depletion from the plasma due to voltage between the plasma and the cathode. At typical plasma densities and magnetic fields, ion erosion is a relatively small effect. Unless field penetration is severe (see below), it is the magnetic force from the storage inductor current that causes opening in a conventional POS (see B. V. Weber, R. J. Commisso, P. J. Goodrich, J. M. Grossman, D. D. Hinshelwood, P. F. Ottinger, and S. B. Swanekamp, "Plasma opening switch conduction scaling," Phys. Plasmas, vol. 2, pp. 3893-3901, 1995). The switch opens, rather than simply translating a slug of plasma, largely because the plasma mass density is non-uniform across the gap. The non-uniform plasma mass density causes an axial component to the current sheet, with a corresponding radial force on the plasma. To a lesser extent, there is plasma shearing due to the variation of magnetic field with radius in the coaxial transmission lines typically used. Because the opening mechanism (storage inductor current) is applied continuously while the switch is closed, it is solely plasma inertia that keeps the conventional switch closed. This means that keeping a switch closed for longer times requires higher plasma mass. For a given conventional POS geometry and drive current, the opening rate will be inversely proportional to conduction time.
While the plasma is conducting current, it is possible for the drive current magnetic field to penetrate into the plasma. This happens when current passes through plasma and the cathode surface emits electrons. The penetration mechanism is replacement of plasma electrons with flux-carrying electrons emitted from the cathode conductor. Because these electrons essentially drift in the E.times.B direction, this is often called Hall penetration (see A. S. Kingsep, Y. V. Mokhov, and K. V. Chukbar, "Nonlinear skin effect in plasmas," Sov. J. Plasma Phys., vol.10, pp. 495-499,1984 and S. B. Swanekamp, J. M. Grossman, A. Fruchtman, B. V. Oliver, and P. F. Ottinger, "Particle-in-cell simulations of fast magnetic field penetration into plasma due to the Hall electric field, " Phys. Plasma, vol. 3, pp. 3556-3563, 1996). An understanding of field penetration is important for determining the plasma density required for the triggered switch concept.
Since the electrons in the injected plasma have zero canonical angular momentum, magnetic field cannot penetrate into that region unless the electrons are pushed away (bulk plasma translation) or replaced, since there is negligible momentum transfer from electrons to the ions. However, electrons emitted from the cathode can have non-zero canonical angular momentum because of momentum transfer to the cathode conductor. Magnetic field penetrates the plasma at the rate plasma electrons are replaced. Since both plasma electrons and cathode electrons carry current, the penetration rate varies with time. The velocity of the replacement front (penetration) is: ##EQU1##
Here I.sub.pe is the current in plasma electrons only, r is the average switch radius, n.sub.e is the plasma electron density, e is the electron charge, and g is the mechanical gap in the switch region. Initially, plasma electrons carry the entire generator current. As the plasma electrons are replaced, cathode electrons carry more current and the penetration slows.
Assuming that the penetration rate is proportional to the number of plasma electrons remaining, one can derive an expression for the position of the magnetic field penetration front as a function of time: ##EQU2##
with EQU Q.sub.p =2.pi.r.multidot.n.sub.e e.multidot.g.multidot.x.sub.0 (3)
x is the distance into the plasma region into which field has penetrated, I.sub.gen is the generator current, and x.sub.0 is the initial axial length of the plasma. Q.sub.p is the total ion charge in the plasma. The combined charge of plasma electrons and beam electrons is equal and opposite to the ion charge. The plasma ion charge changes (though usually not dramatically) as ions leave the plasma. This approximation assumes the plasma mass distribution is unchanging. Compared to particle-in-cell simulation data, this simple model somewhat over-predicts the replacement rate because cathode electrons carry a higher fraction of current than the ratio of cathode electrons to total electrons.
The magnetic field penetration time constant, ##EQU3##
gives the exponential folding time based on the above model. At one time constant, the magnetic field has penetrated approximately 37 percent of the axial length of the plasma.
For a coaxial switch of 10-cm radius, 5-cm electrode gap, and axial switch length of 15 cm, and doubly ionized plasma at 10.sup.21 ions/m.sup.3, the penetration time constant is 1.5 .mu.s at 1 MA drive current. Thus in such an experiment with 500 ns or longer drive time, there is considerable plasma mass left behind the magnetic piston. The voltage in the switch region cannot rise appreciably until the charge density in the gap decreases much below the initial density. These ions can only be removed by acceleration across an electric sheath, at the expense of more energy than sweeping them in a magnetic snowplow. Increasing the plasma ion number density reduces field penetration but raises the mass that must be moved for opening. A viable approach to improving opening switch performance would be to reduce the opening field rise time so that penetration is unimportant for reasonable plasma densities.
Another important vacuum opening switch parameter is the amount the switch opens. The fraction of the anode-cathode gap cleared of plasma determines the efficiency of the POS. One way to infer the effective gap cleared of plasma is to measure voltage and electron flow downstream of the POS and compute the consistent vacuum impedance. This technique is a flow impedance (see C. W. Mendel, Jr. and S. E. Rosenthal, "modeling magnetically insulated devices using flow impedance," Phys. Plasmas, vol. 2, pp. 1332-1342, 1995 and C. W. Mendel, Jr., M. E. Savage, D. M. Zagar, W. W. Simpson, T. W. Grasser, and J. P. Quintenz, "Experiments on a current-toggled plasma-opening switch," J. Appl. Phys., vol. 71, pp. 3731-3746, 1992) calculation. The flow impedance of a section of magnetically insulated transmission line is ##EQU4##
where Z.sub.f is the flow impedance, V is the voltage, I.sub.ua is the anode current upstream of the section and I.sub.dc is the cathode current downstream of the section.
Flow impedance considers axial electron flow, which is important in magnetically insulated systems. For this reason, flow impedance may be used as a measure of opening switch performance, instead of other commonly used parameters such as voltage or resistance. For efficiency, the effective impedance of the opening switch must be higher than the load impedance, so it is the load and not the opening switch that determines voltage. Another common technique is modeling the POS as a radial resistor. This is not generally useful because the calculated resistance varies dramatically with both load impedance and current monitor location, due to axial current in vacuum-flowing electrons. Flow impedance is equally valid in situations where there is externally applied magnetic fields (see C. W. Mendel, Jr., J. P. Quintenz, S. E. Rosenthal, D. B. Seidel, R. Coats, and M. E. Savage, "Experiments on insulation of relativistic electron flows in oblique magnetic fields," IEEE Trans. Plasma Sci., vol. 17, pp. 797-800, 1989).
A desirable opening switch for an inductive energy store system is one that opens quickly compared to the output pulse width, and opens far enough to allow efficient energy transfer to the load. Further, since the POS is the final stage of pulse compression, a system that allows temporal synchronization of the output pulse is also desirable. The command-triggered plasma opening switch described below is designed to improve performance as well as introduce the ability to actively trigger its opening.